Snapshot hyperspectral imager for emission and reactions (shear)

ABSTRACT

A spectral imaging system includes an objective lens system, an optical splitter, a dispersion system, and an optical combiner. The optical splitter is arranged to be in an optical path of an object being imaged through the objective lens system to provide an imaging optical path and a spectrometer optical path. The dispersion system is arranged in the spectrometer optical path. The optical combiner is arranged in the imaging optical path and a path of dispersed light from the dispersion system to combined dispersed light with a corresponding optical image of the object.

CROSS-REFERENCE OF RELATED APPLICATION

This application claims priority to U.S. Provisional Application No.62/961,981, filed Jan. 16, 2020, the entire contents of which are herebyincorporated by reference.

FEDERAL FUNDING

This invention was made with government support under grant numbersHDTRA1-18-1-0016 and HDTRA1-15-1-0006 awarded by the Defense ThreatReduction Agency. The government has certain rights in the invention.

BACKGROUND Related Art

Hyperspectral imagers sample the spectral irradiance of a scene, I(x, y,λ), where x, y, and λ are respectively the x dimension, y dimension, andwavelength λ, to form a three dimensional (x, y and λ dimensions)dataset known as a hyperspectral datacube. Given the two-dimensional(2D) nature of image sensors, the information contained in the spectralirradiance is either captured as a sequence of 2D datasets (i.e.scanning spectral imaging), or in a single 2D frame (i.e. snapshot)which can be decomposed into a cube during the post processing stages.

Snapshot hyperspectral imaging is a pivotal technology which can providean immense amount of information about the temperature, composition, andrapid interactions of various material systems. Current commerciallyavailable hyperspectral imagers are either integrated into the imagesensors, or require slow, scanning spectral filter banks. This limitstheir utility in high speed material synthesis and characterization.

Hyperspectral imagers may be applied to materials systems for analysis.Materials systems which react at extreme speeds and temperatures, suchas the combustion of metals fuels like Al, B, Mg, Zr, Ti, etc., arefundamentally difficult to diagnose due to the rapid, transient natureof their reactions. These pure metal fuels have been used in energeticmaterials formulations for decades due to their high enthalpy ofcombustion on a gravimetric and volumetric basis. There is an increasingneed for sophisticated diagnostics to understand and characterizenext-generation metal fuels, which are being developed with variationsof particle size, chemistry, and other modifications via methods such asalloying, surface coating, composite formation, etc. Metal fuels canvary widely in their burn time, temperature, emission spectra, gaseousspecies production, affinity for various oxidizers, and behaviors indifferent environments, and these properties can be widely tuned undervariations of the material. To compensate for the increasing complexityof the materials systems, there is a need for increased spectroscopicinformation to understand the fundamental mechanisms of their burn,particularly in high-throughput methods.

Hyperspectral imagers may be applied more broadly to characterization ofhot molecules and materials systems such as solid propellants, liquidfuel droplet combustion, carbon/soot combustion, as well as elementslike Si, and B.

Modern spectroscopic analysis tools have evolved greatly from simplespatial and temporally integrated signals. Glumac, et al. have utilizedan imaging spectrometer which can provide spectroscopic information ofAl combustion at high speeds along a particular axis within a flame[Glumac, N., Absorption Spectroscopy Measurements in Optically DenseExplosive Fireballs Using a Modeless Broadband Dye Laser, Appl.Spectrosc. 2009, 63, 1075; DOI: 10.1366/000370209789379268]. They havealso enhanced these methods by introducing laser-absorption to penetratethrough the optically dense flames. Further, Johnson et al. havecombined the technique with high-speed videography to obtainsimultaneous spectroscopy and imaging by utilizing a second camera[Johnson, S.; Clemenson, M.; Glumac, N., Simultaneous Imaging andSpectroscopy of Detonation Interaction in Reactive and EnergeticMaterials, Appl. Spectrosc. 2017, 71, 78; DOI:10.1177/0003702816661726]. This technique provides good spectral andtemporal resolution (2.4 Å and 100 ns, respectively), but lacks spectralinformation from outside of the spatial region of the slit. Therefore,it is not suited for sparse reactions or for burning particulates thatare in motion within the field of view of the camera, such as those thatmight be present in fragmentation events or material reacted on a wire.Other optical pyrometry methods use filtered photomultipliers to measurethe burn temperature and time of individual particles, lack theparticle-to-particle interactions that are present in larger-scalesystems and cannot capture the behavior of many individual particles.

Imaging pyrometry, which utilizes existing high-speed camera systems,has also shown success, and includes variants of two- and three-colorsystems. In general, these techniques involve utilizing ratios of twohigh-speed cameras' RGB (red, green, blue) pixel values, accounting forthe cameras' response at various wavelengths, and calibrating thesevalues against a known standard such as a furnace or tungsten lamp.Though optical pyrometry can measure temperature variations in space andtime, in many cases it sacrifices any spectral information present inthe event due to filtering. Further, since the temperature measurementsare made from integrated RGB pixel intensities, they can be skewedsignificantly due to the presence of emission species such as AlO, whichhave well-studied bands in the visible region. Therefore, these methodsmust be used tactfully in metal-containing systems.

What is needed is to combine the methods of spectral imaging and opticalpyrometry in high-speed, spatially resolved spectroscopy which canprovide (in a single video) a large statistical dataset on the burntime, temperature, and spectra of these materials, and which can beapplied to a wide variety of applications. For example, the combinationmay assess dynamic temperature variation for individual particles,gaseous combustion species concentrations such as AlO, MgO, etc. andtheir timing, and the burn time of fireballs and particles. Further,scalable methods are desired that have the ability to both zoom-in toanalyze micron-scale events such as the temperature and stand-offdistance of individual, micron-scale Al-based particles burning in aflame and zoom-out to analyze larger scale events such as explosivefireball. Further, the methodologies may be adaptable and easy to deployon existing high-speed cameras.

SUMMARY

According to certain embodiments, a spectral imaging system is provided.The spectral imaging system may comprise: an objective lens system; anoptical splitter arranged to be in an optical path of an object beingimaged through said objective lens system to provide an imaging opticalpath and a spectrometer optical path; a dispersion system arranged inthe spectrometer optical path; and an optical combiner arranged in saidimaging optical path and a path of dispersed light from said dispersionsystem to combined dispersed light with a corresponding optical image ofthe object.

According to certain embodiments, there is provided a method of spectralimaging. The method comprises: imaging an object through an objectivelens system along an optical path; splitting the optical path of theobject being imaged to provide an imaging optical path and aspectrometer optical path; imaging light in the imaging optical path;dispersing light in the spectrometer optical path; and combining thedispersed light from the spectrometer optical path with a correspondingoptical image of the object from the imaging optical path.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objectives and advantages will become apparent from aconsideration of the description, drawings, and examples.

FIG. 1 is a schematic of a spectral imaging system according to someembodiments.

FIG. 2A is a schematic of a spectral imaging system with a reflectivegrating according to some embodiments.

FIG. 2B is a schematic of a spectral imaging system with a transmissivegrating according to some embodiments.

FIGS. 3A and 3B illustrate examples of coded masks according to someembodiments.

FIGS. 4A-4F illustrate the registration process according to someembodiments. FIGS. 4A and 4B show the checkerboard images correspondingto a 488 nm laser, and white light illumination of the main and sidechannels, respectively. FIG. 4C illustrates overlapping patterns afterimage transformation. FIGS. 4D-4F shows how the transformation isapplied to images of the reacting particles and the subsequent mapping.

FIG. 4D is a schematic of the two channels (main and side), and how theysimultaneously appear on the image sensor. FIG. 4E illustrates the rawdata, while FIG. 4F shows a co-registered image.

FIGS. 5A-5E illustrate a flow diagram of a spectra recovery processaccording to some embodiments, where FIG. 5A shows a combustion scenehaving an irradiance, FIG. 5B is a scene schematic, FIG. 5C illustratesa mask or localized image regions or spots, FIG. 5D shows a side channelimage, which has spots corresponding to FIG. 5C, and FIG. 5E shows mainchannel spectra.

FIGS. 6A-6G demonstrate the process used to estimate a burning particletemperature according to some embodiments. FIG. 6A is a representativeimage of an Al—Zr reaction with the particle of interest circled. FIG.6B shows the SHEAR response to a Halogen lamp on blue (darker line) andgreen (lighter line) sensor channels. respectively. FIG. 6C shows a lineimage of the particle under study. FIG. 6D shows a combined spectra ofthe particle. FIG. 6E shows a calibrated particle spectra afterfactoring out the contribution from the Halogen lamp. FIG. 6G shows theratio of the black-body intensity ratio at 450 nm to 500 nm.

FIG. 7A illustrates an image of a first particle moving across a fieldof view over time, where the particle is circled in white, according tosome embodiments. FIG. 7A further illustrates the spectra from the firstparticle as a function of time as the first particle moves across thefield of view.

FIG. 7B illustrates an image of a second particle moving across a fieldof view over time, where the particle is circled in white, according tosome embodiments. FIG. 7B further illustrates the spectra from thesecond particle as a function of time as the second particle movesacross the field of view.

FIG. 8 illustrates the temperature evolution for a representativeparticle which stays within the imaging field of view for 180 frames,according to some embodiments.

FIG. 9A illustrates the temperature statistics for all the particlesduring their entire lifetime, according to some embodiments.

FIG. 9B illustrates how all the particles in a given frame aredistributed across the temperature range, according to some embodiments.

FIG. 10 illustrates several representative frames (101, 144, 218, 296)of a high speed video of particles with temperature mapping, accordingto some embodiments.

DETAILED DESCRIPTION

Some embodiments of the current invention are discussed in detail below.In describing embodiments, specific terminology is employed for the sakeof clarity. However, the invention is not intended to be limited to thespecific terminology so selected. A person skilled in the relevant artwill recognize that other equivalent components can be employed andother methods developed without departing from the broad concepts of thecurrent invention. All references cited anywhere in this specification,including the Background and Detailed Description sections, areincorporated by reference as if each had been individually incorporated.

According to some embodiments, a snapshot, randomly sampled imager isprovided, which may be called Snapshot Hyperspectral Imager for Emissionand Reactions (SHEAR). This system simultaneously captures a given sceneof interest and its corresponding spatially-resolved spectra on a single2D image sensor. The system may be low cost, wavelength agnostic, andcan be paired with many commercially available camera systems. SHEARsystem may include a combination of novel optical hardware and softwaresystems which provide a low cost, versatile method for high throughput,image-based, hyperspectral analysis and characterization of materialsystems in applications such as combustion research, thermal spraycoating, and laser additive manufacturing, for example.

SHEAR system may provide hyperspectral imaging to garner temporal andspatially resolved spectroscopy with, for example, an off-the-shelfhigh-speed camera system, or a lower speed camera. The term “high-speedcamera” is intended to have a broad meaning to include existing orfuture developed high-speed cameras that can be stand-alone devices thatare attached to or integrated into the current spectral imaging system,or can be specially provided detectors and electronics designed for thecurrent system.

The SHEAR system in some embodiments is ideally suited for bright, fast,sparse, and emissive reactions such as those with metal fuels and otherenergetic materials. In some embodiments, the SHEAR system may be usedto measure both the spectra and temperature for hundreds of individualburning Al/Zr composite metal particles in a single video (series ofimages). In some embodiments, for example, SHEAR may be used to analyzeAl/Mg/Zr composite particles which burn rapidly in a larger deflagrationplume. SHEAR is adaptable, portable, inexpensive, and easily toimplement using a single camera, which may be high speed. Ultimately,due to the flexibility of the SHEAR system, the system may be employedin a variety of applications, such as in metallized and enhancedblast/thermobaric explosives, materials for bio- and chemical-agentdefeat, reactive fragments, fundamental science of metal or thermitecombustion, other propellant and pyrotechnic systems, and any systemcontaining hot particles and/or gaseous species that emit radiation, forexample.

A “high-speed camera” is not a requirement for this system. SHEAR can beused with any commercial image sensor in the visible, and infraredregimes. Frame rate can range from sub-Hz to MHz depending on the choiceof camera, or other image sensor.

The SHEAR system combines the methods of optical pyrometry andhigh-speed, spatially resolved spectroscopy and provides (in a singlevideo) a large statistical dataset on the burn time, temperature, andspectra of various material systems. Notably, the developed technologyprovides a means to assess dynamic temperature variation for individualparticles, gaseous combustion species concentrations such as AlO, MgO,etc. and their timing, and the burn time of fireballs and particles.Further, the SHEAR system may include an image processing systemconfigured to simultaneously measure the size, position, morphology,temperature, or emission spectra of reacting materials or molecules,solid propellants, liquid fuel droplet combustion, carbon/sootcombustion, Si or B. Further, for the SHEAR system, informationregarding combined dispersed light with a corresponding optical image ofthe object may include data from propellants, pyrotechnics, metal andnon-metal fuels, carbon/soot combustion, high explosives, metallizedexplosives, molecules, or impact and fragmentation high speedthermography.

FIG. 1 illustrates a spectral imaging system 100 according to someembodiments. The spectral imaging system 100 may include an objectivelens system 120, which is arranged to receive light from an object 10and to image the received light ultimately to a two-dimensional imagesensor 140, which may be a camera, such as a high speed camera.According to some embodiments the two-dimensional image sensor 140 isseparate from spectral imaging system 100. Alternatively, thetwo-dimensional image sensor 140 may be a part of the spectral imagingsystem 100.

The spectral imaging system 100 further includes an optical splitter BS1which is arranged to be in an optical path of the object 10 being imagedthrough the objective lens system 120 to provide an image optical path,and a spectrometer optical path. In FIG. 1 , the imaging optical path isthe path, 120, BS1, M1, M2, BS2. The spectrometer optical path is thepath 120, BS1, 130, BS2. In the arrangement of FIG. 1 , the opticalsplitter BS1 directs the light collected to provide light along theoptical path to a first mirror M1, and to a second mirror M2, whichdirects the light along the imaging optical path to the optical combinerBS2. Further, in the arrangement of FIG. 1 , the optical splitter BS1images the light collected to provide light to the dispersion system130, which disperses the light into a spectrum of wavelengths, whichdispersed light is directed to the optical combiner BS2, to be combinedwith the light from the imaging optical path, and directed to thetwo-dimensional image sensor 140. The optical combiner BS2 may be anon-polarizing 50:50 beam splitter cube (Thorlabs BS013), for example.The optical splitter BS1 may be one of a dichroic prism or a dichroicmirror, for example. The components of the spectral imaging system 100may be arranged such that the imaging optical path follows a sidesecondary path (side channel), while the spectrometer optical pathfollow a primary path (main channel) such as shown in FIG. 1 .

The dispersion system 130 may include, for example, a transmissiongrating, or a reflective grating, or a prism. The grating or prism maybe arranged to disperse light into a range as desired. The dispersionsystem 130 may include a reflecting or transmission dispersion elementarranged to provide first order diffracted light to the optical combiner140. The system may include other components beyond what is shown inFIG. 1 .

The spectral imaging system 100 may further include an image processingsystem 150 including, for an example, a processor 152 and a memory 154.The processor 152 may perform data analysis based on data or otherinformation from the two-dimensional sensor 140, and based on dataanalysis procedures stored in the memory 154, which may be anon-transitory computer readable medium. The procedures may include, forexample, wavelength calibration, registration of points of the imagefrom the imaging optical path with corresponding spectral data from thespectrometer optical path, tracking localized image regions on theimage, and recovery of spectra associated with respective of thelocalized image regions, where these techniques are described furtherbelow.

FIGS. 2A and 2B illustrate spectral imaging systems 200 a and 200 b,respectively, according to some embodiments. FIG. 2A illustrates asystem where the dispersion system 130 includes a reflective grating,while FIG. 2B illustrates a system where the dispersion system 130includes a transmission grating.

The imaging systems 200 a and 200 b for FIGS. 2A and 2B are comprised oftwo optical paths (spectrometer optical path and imaging optical path)in a similar fashion to FIG. 1 . Each of the two imaging systems 200 aand 200 b may be disposed between a sensor lens 215, such as a macrocamera lens, and the two-dimensional image sensor 140, such as a highspeed camera or CCD array. The imaging optical path may in someembodiments capture a conventional high speed video, while thespectrometer optical path may capture a high resolution spectralresponse of the object 10, or objects, in a scene. In some embodiments,the sensor lens 215, such as a field adaptable camera lens, forms animage of the hyperspectral scene at an intermediate image plane 220located in front of spectral imaging systems 200 a or 200 b. Thespectral imaging systems 200 a or 200 b may include a tunable mechanicalslit 260 (i.e. aperture) diposed on this intermediate image plane 220 inorder to ensure that the spectra associated with the entire field ofview falls within the sensor 140. The objective lens L1 collects lightfrom the intermediate plane 220. The primary path (main channel orspectrometer optical path) in the system is responsible for multi-pointspectral decomposition via the dispersion system 130.

For the spectrometer optical path, four bi-convex lenses (L1, L2, L3,L6) may be laid out in a 4-f configuration, for example in order toconstruct two 1:1 relay paths between the primary image plane, which islocated at plane 220 in FIG. 2B, and the two-dimensional image sensor140. Depending on the choice of dispersion system 130 the spectralimaging systems 200 a and 200 b can be used for imaging pyrometry, orhigh resolution, spatially resolved molecular emission and absorptioncharacterization, for example. The optical splitter (BS1), which may bea beam splitter, may be used in the first relay stage to direct afraction of the incoming light towards the imaging channel (i.e. sidechannel or imaging optical path). The desired hyperspectral scene fromthe main channel undergoes spectral decomposition within the secondrelay stage. This stage may incorporate a blazed diffraction grating inLithrow configuration for the dispersion system 130, for example. Theoptical combiner BS2, for example a non-polarizing beam combiner, may beused to redirect light from both channels towards the image sensor 140.In a similar fashion to the main channel (spectrometer optical path),the side channel (imaging optical path) in the system may be made of two4-f relay stages comprising bi-convex lenses L1, L4, L5, and L6,respectively. The spectral imaging systems 200 a and 200 b may include acombination of filters F1 and F2, for example, arranged as neutraldensity (ND) filters and color filters in order to prevent imagesaturation while capturing bright events.

Alternative embodiments are considered. For example, the opticalcombiner BS2 may include a combination of transmission gratings, and/orprisms as a diffractive element. In an alternative configuration,bi-convex lenses can be replaced with curved mirrors. Further thespectral imaging systems 200 a and 200 b may use any image sensor 140regardless of the spectral range or the color choice of the image sensor140.

The spectral imaging systems 100, 200 a or 200 b may be operated indifferent modes according to the nature of the scene to be investigated,in particular, according to the density of the scene. For example, thespectral imaging systems may be operated in a sparse and dynamic scenemode. In this mode the image includes bright, and/or emissivemicro-particles which may behave as agile optical pinholes. The opticalimage, as well as the spectral response from each micro-particle iscaptured simultaneously via the image sensor 140. Overlapping spectramay be deconvolved using interative algorithms by exploiting informationobtained from the side channel (image optical path) as well as temporalevolution of individual particles.

The spectral imaging systems may be operated in a dense and dynamicscene mode using a sparse set of randomly distributed apertures tosample many points in the related scene simultaneously, such as by usinga mask. The distribution of the apertures can be tailored for differentstudies in accordance with the nature and spread of the hyperspectralscene under study. In one embodiment, the coded masks are printed onoptically clear materials that can be inserted into the field of viewaccording to the experimental scene. As shown in FIGS. 2A and 2B, a mask270 may be incorporated into the spectral imaging systems 200 a and 200b. The mask 270 may be coded or otherwise.

FIGS. 3A and 3B illustrate examples of coded masks 300 a and 300 b,respectively. Each of the masks include a number of apertures 310arranged on the mask. The coded masks may be printed on optically clearmaterials.

Image Registration

The image processing system 150 may be configured to register spectralinformation with at least one of localized image regions or spots frominformation received from the two dimensional sensor 140. One feature ofthe spectral system according to certain embodiments is the ability toobtain wide-field (i.e. image optical path) and spectral images of thescene, via the spectrometer optical path, under study side by side.Given the complex nature of emission events it is beneficial tospatially register the side channel (image optical path) images to thespectral data (spectrometer optical path). Image registration may becarried out in two steps according to some embodiments:

In step 1 an object containing uniformly spaced checkerboard patterns isplaced in the system object plane. In step 2 images from both channelsare captured. An affine transform function, such as from MATLAB, may beused in order to map the side channel data to the spectral channel. Animage registration transformation matrix may be obtained matchingcheckerboard corners in the two channels.

FIGS. 4A-4F illustrate the registration process. FIGS. 4A and 4B showthe checkerboard images corresponding to a 488 nm laser, for example,and white light illumination of the main and side channels,respectively. In order to ensure uniform, speckle free imaging of themain channel a rotating engineered diffuser, such as Thorlabs ED1-C50,may be used in front of the laser source. The transformation matrix wasobtained in post processing stage where 6-12 matching corners wereidentified between the main and side channel images. A fitting function,such as MATLAB's fitgeotrans function, may be used to map the sidechannel to the main channel. FIG. 4C illustrates overlapping patternsafter image transformation. While mapping is carried out at 488 nmwavelength in some embodiments, the mapping can be carried over to anyother wavelength by a linear shift proportional to the image sensor 140(camera) pixel to wavelength mapping. FIGS. 4D-4F shows how thetransformation is applied to images of reacting PVD particles and thesubsequent mapping.

Particle Tracking

Particles in the image may be tracked through multiple frames over timeaccording to some embodiments. In the case of a particle moving aroundor through the image frame, the particle position may be tracked overtime. In some embodiments, the tracking may use the spatial sparsityover multiple frames and reconstruct the full lifecycle of individualparticles.

According to some embodiments of tracking, the particles are identifiedon every frame by applying a gaussian filter and thresholding, followedby a basic peak search that locates the centroid of every particle. Inaddition to the centroid, the particle size data may be collected as acircular area and circumference.

In order to track the particles over multiple frames, identifiedparticles may be linked together based on their relative position acrosssuccessive frames. This is achieved by applying an iterative algorithmthat uses only the particle centroid positions and a maximum searchradius. The search radius is determined by the maximum particle speedthat can be tracked based on the pixel to particle size ratio.

According to some embodiments, the particle tracking algorithm mayexecute the following steps:

1. Particles are initialized as starting positions for tracking in thefirst frame n=1.

2. Particle positions in frame n+1 are compared to particle positions inframe n.

-   -   (a) The minimum difference between positions in frame n and n+1        is found.        -   (i) If the difference is less than the maximum search            radius, particle from frame n+1 is assigned to a            corresponding particle in frame n and the position pair is            removed from the particle position index. (a) is then            repeated.        -   (ii) If the difference is greater than the maximum search            radius, break.    -   (b) All remaining particles on frame n are removed, and all        remaining particles on frame n+1 are initialized as starting        positions, break.

3. Repeat step 2 with the next frame, n=n+1.

Spectra Recovery

Spectra from localized image regions or spots, such as particles, mayoverlap with each other. In order for the spectra for a particularparticle to be recovered, the spectra may be deconvolved and spectralde-multiplexing may thus be performed. FIGS. 5A-5E illustrate a dataflow diagram, where FIG. 5A shows a combustion scene having anirradiance, FIG. 5B is a scene schematic, FIG. 5C illustrates a mask orlocalized image regions or spots, FIG. 5D shows a side channel image,which has spots corresponding to FIG. 5C, and FIG. 5E shows main channelspectra. The scene with irradiance I(x, y, λ) is relayed over to eithera sparse mask, M(x, y, λ) which samples multiple points across the fieldof view, or a fully transmissive mask with spots from the sampled scene,where x is along the dispersion direction, y is perpendicular to x, andλ is the light wavelength. Given that the dispersion is along the xdirection of the image sensor 140, the sampled scene should be sparsealong this axis according to certain embodiments. The sparsely sampledpoints are then mapped onto the image sensor 140 via the dispersivesystem 130 (e.g. diffraction grating), in the main channel, and via a4-f relay in the side channel. Signals obtained from the main and sidechannels are therefore given by, integral (I(x×τ_(n), y,λ_(n))×M(x×τ_(n), y, λ_(n))dn), and I(x, y, λ)×M(x, y) respectively,where τ_(n) represents the pixel shift at wavelength due to thedispersion. The task is then to recover I(x, y, λ_(n)) from the abovetwo measurements based on the main and side channels. τ_(n) and λ_(n)can be extracted from the experimental parameters.

The sparsity assumption implies that only N<<P pixels are active (i.e.have mask with unity transmission) in any given vertical line, where Nmay be the number of pixels in the side channel associated with thetransmissive features (apertures 310) in the mask 300, or the number ofbright burning particles, and P may be the total number of image pixels.The problem can then be formulated using matrix notations as follows:

$\begin{matrix}{\begin{bmatrix}y_{1} \\y_{2} \\ \cdot \\ \cdot \\ \cdot \\y_{M}\end{bmatrix}_{M \times P} = {\begin{bmatrix}1 & 0 & \ldots & & & 0 \\0 & 1 & \ldots & & & 0 \\ & & \cdot & & & \\ & & \cdot & & & \\ & & \cdot & & & \\0 & 0 & \ldots & 1 & 1 & 1\end{bmatrix}_{M \times P} \times \begin{bmatrix}x_{1} \\x_{2} \\ \cdot \\ \cdot \\ \cdot \\x_{N}\end{bmatrix}_{N \times P}}} & (1)\end{matrix}$

Y and X are the measurement and the spectral information respectively.The binary matrix, denoted as A, represents the active mask elements.Each row in the X matrix is padded with zeros in accordance to the knownspectral extent of the signals, and the spectral centroid which isobtained from the side channel. Our recovery algorithm attempts to solvefor X such that Y−AX is minimized.

Specifically, the side channel can then be used to track particleposition over time to generate the particle position map P (x, y, t)where every particle exists at some point in space and time p_(n) (x, y,t) where n is the particle number. The main channel image can bedescribed as a linear combination of all the particles spectra. This canbe described simply as

Y=PS  (2)

where Y is the main channel image and S are the particles' spectra. Fromthis formulation we note the similarity to the standard compressedsensing equation of Y=AX, where Y are the compressed measurements, A isknown as sensing matrix, and X is the signal of interest. Compressedsensing theory states that a sparse signal X can be reconstructed with asmall number of measurements Y, that are the inner product between thesignal and the A matrix. This technique can then be used to bothde-multiplex overlapping particle spectra and remove background noise,taking full advantage of compressed sensing techniques.

To recover the spectra of a particle at index k, we select compressedmeasurements to be the rows of the main channel image around which killuminates the sensor, y_(k)=Y(λ, p_(k)(x, y, t)>0). Each measurementcontains information that can be used to reconstruct the true spectra ofparticle k over time. The A matrix is constructed using the position ofother particles that exist in the rows occupied by the particle k. Aswell as in a single frame, as the particles moves throughout the fieldof view there are numerous combinations of particle spectra thatilluminate the sensor, generating a pseudorandom A matrix that mapsparticle spectra to the sensor pixels. This can be described as

y _(k) =A _(k) S  (3)

where A_(k) is a sparse matrix that represents all particles that existover the spatial and temporal duration of particle k, over which iscollected the measurements y_(k). The algorithm will come up with thesparsest solution for the particle spectrum S{circumflex over( )}_(k)(λ, t) while maintaining fidelity with the measurements byminimizing y_(k)−A_(k) S . In addition to the denoising effects of thesparse solution, a phantom particle may be added to intelligently removesensor background noise.

The following steps describe how the data is processed includingspectral de-multiplexing according to some embodiments:

1. The side channel is used for particle identification that includesimage thresholding and Gaussian filtering.

2. The particle map P is constructed by tracking particles over theimage frames.

3. The compressed measurements and A matrix for every particle isconstructed using the particle map P and main channel images Y.

4. Compressed sensing algorithm reconstructs the spectral evolution overtime for each particle spectra S.

5. Wavelength calibration gives the blackbody irradiance I andtemperature is determined using curve fitting with a graybody emitter.

Wavelength Calibration and Temperature Measurements

Temperature estimation in imaging may be performed by mapping themeasured spectra to Plank's black-body radiation curve. In order tocarry out the temperature calibration, however, one must account for thespectral response from various optical components, as well as any colorfilters on the sensor 140. FIGS. 6A-6G demonstrates the process used toestimate the burning particle temperature. Upon wavelength calibration,light from a Halogen source is passed through a narrow slit and thespectral response of the SHEAR is recorded on the sensor 140. FIG. 6A isa representative image of an Al—Zr reaction with the particle ofinterest circled. FIG. 6B shows the SHEAR response to the Halogen lampon the blue (darker line) and green (lighter line) sensor channels,respectively. FIG. 6C shows a line image of the particle under study.FIG. 6D shows a combined spectra of the particle. FIG. 6E shows acalibrated particle spectra after factoring out the contribution fromthe Halogen lamp (see FIG. 6F). The line is the linear fit through theparticle spectra while neglecting the contribution from the emissionpeaks. FIG. 6G shows the ratio of the black-body intensity ratio at 450nm to 500 nm. The square indicates the temperature that best matches thefitted linear curve over the burning particle. In order to obtain sourceindependent system response, the lamp images for each channel weredivided by the lamp spectra from a commercial spectrometer FIG. 6F.

Example Applications

Example applications for the SHEAR system include high resolutiondynamic imaging spectroscopy and full color pyrometry. For example, inthe high-resolution mode, the increased dispersion due to a gratingspacing of 1200 line/mm for a diffraction grating provides higherspectral resolution while simultaneously decreasing the wavelength rangesampled due to the fixed area of the sensor. The Al in the materialsused reacts with oxygen to produce the AlO peaks in the blue-greenregion of the spectrum. FIGS. 7A-7B show these peaks exhibited by twoburning particles. The molecular AlO bands are well studied andrepresent vapor-phase combustion of the Al species within the particles.Greybody fitting over such a short wavelength region is possible but cancause larger uncertainties in the temperature measurement relative tothe full-color mode. FIG. 7A illustrates an image of a first particlemoving across a field of view over time, where the particle is circledin white. FIG. 7A further illustrates the spectra from the firstparticle as a function of time as the first particle moves across thefield of view. FIG. 7B illustrates an image of a second particle movingacross a field of view over time, where the particle is circled inwhite. FIG. 7B further illustrates the spectra from the second particleas a function of time as the second particle moves across the field ofview.

In the full-color pyrometry mode, the wavelength range may be expanded(at the expense of resolution) to include light in the red visibleregion, allowing for lower temperatures to be measured and a largerdynamic range for graybody fitting. FIG. 8 shows the temperatureevolution for a representative particle which stays within the imagingfield of view for 180 frames. The videos were captured using a 300lines/mm diffraction grating and temperature was estimated by fittingthe particle's radiation patterns to a theoretical graybody. The curvefitting was accomplished using MATLAB′sfittype function. The function isa nonlinear least square minimization method based on theLevenberg-Marquardt algorithm. Since the particle's emissivity isunknown, the fitting algorithm estimates the emissivity and temperaturewhich best represented the measured curve. As is seen in FIG. 8 , theparticle experiences a drop in temperature (prior to a microexplosion).These microexplosion events are well studied in related works, and thissystem allows for correlation of morphological changes such asmicroexplosions with the temperature of the particle/flame at the samemoment. The microexplosion is followed by a sudden energy release whichmanifests itself as a 400 K rise in the temperature.

FIG. 9A shows the temperature statistics for all the particles duringtheir entire lifetime. On average most particles reach temperaturesaround 2300 K. Higher temperatures in this system are usually achievedduring vapor-phase combustion (e.g., corresponding to AlO formation). Itis worth noting that while almost every particle experiencesmicro-explosions, not every micro-explosion falls in the imaging fieldof view. FIG. 9B shows how all the particles in a given frame aredistributed across the temperature range.

The temperature information in FIGS. 9A and 9B can be mapped onto theside channel (optical video) images of the particles as they are inmotion through the video frame. Several representative frames of ahigh-speed video with this temperature mapping completed are shown inFIG. 10 .

The embodiments illustrated and discussed in this specification areintended only to teach those skilled in the art how to make and use theinvention. In describing embodiments of the invention, specificterminology is employed for the sake of clarity. However, the inventionis not intended to be limited to the specific terminology so selected.The above-described embodiments of the invention may be modified orvaried, without departing from the invention, as appreciated by thoseskilled in the art in light of the above teachings. It is therefore tobe understood that, within the scope of the claims and theirequivalents, the invention may be practiced otherwise than asspecifically described.

We claim:
 1. A spectral imaging system, comprising: an objective lenssystem; an optical splitter arranged to be in an optical path of anobject being imaged through said objective lens system to provide animaging optical path and a spectrometer optical path; a dispersionsystem arranged in said spectrometer optical path; and an opticalcombiner arranged in said imaging optical path and a path of dispersedlight from said dispersion system to combined dispersed light with acorresponding optical image of said object.
 2. The spectral imagingsystem according to claim 1, wherein said dispersion system comprises areflecting dispersion element arranged to provide first order diffractedlight to said optical combiner.
 3. The spectral imaging system accordingto claim 1, wherein said optical splitter is one of a dichroic prism ora dichroic mirror.
 4. The spectral imaging system according to claim 1,further comprising a high-speed camera arranged to receive said combineddispersed light with said corresponding optical image of said object. 5.The spectral imaging system according to claim 4, wherein saidhigh-speed camera is arranged to capture said dispersed light andcorresponding optical image in a single camera frame.
 6. The spectralimaging system according to claim 4, further comprising an imageprocessing system configured to communicate with said high-speed camerato receive information regarding said combined dispersed light with saidcorresponding optical image of said object.
 7. The spectral imagingsystem according to claim 6, wherein the image processing system isconfigured to simultaneously measure the size, position, morphology,temperature, or emission spectra of reacting materials or molecules,solid propellants, liquid fuel droplet combustion, carbon/sootcombustion, Si or B.
 8. The spectral imaging system according to claim6, wherein said image processing system is further configured toregister spectral information with at least one of localized imageregions or spots from said information received from said high-speedcamera.
 9. The spectral imaging system according to claim 8, whereinsaid image processing system is further configured to track over time aposition of each of said at least one of localized image regions orspots from said information received from said high-speed camera. 10.The spectral imaging system according to claim 9, wherein said imageprocessing system is further configured to track the position of each ofsaid at least one of localized image regions or spots over a series offrames.
 11. The spectral imaging system according to claim 9, whereinsaid image processing system is further configured to recover spectralinformation registered with each of said at least one of localized imageregions or spots from said information received from said high-speedcamera.
 12. The spectral imaging system according to claim 11, whereinthe image processing system is arranged to process the spectralinformation data in the form of 3-dimensional hyperspectral cubes, andto recover the spectral information registered with each of said atleast one of localized image regions or spots by deconvolution usingspectral de-mixing.
 13. The spectral imaging system according to claim6, wherein said image processing system is further configured to providea temperature map corresponding to said spectral information.
 14. Thespectral imaging system according to claim 1 further comprising atransmissive mask arranged to randomly sample a field of view in thepath of dispersed light.
 15. The spectral imaging system according toclaim 6, wherein said information regarding said combined dispersedlight with said corresponding optical image of said object includes datafrom propellants, pyrotechnics, metal and non-metal fuels, carbon/sootcombustion, high explosives, metallized explosives, molecules, or impactand fragmentation high speed thermography.
 16. A method of spectralimaging comprising: imaging an object through an objective lens systemalong an optical path; splitting the optical path of the object beingimaged to provide an imaging optical path and a spectrometer opticalpath; imaging light in the imaging optical path; dispersing light in thespectrometer optical path; and combining the dispersed light from thespectrometer optical path with a corresponding optical image of saidobject from the imaging optical path.
 17. The method according to claim1, further comprising receiving information regarding said combineddispersed light with said corresponding optical image of said object.18. The method according to claim 17, further comprising registeringspectral information with at least one of localized image regions orspots from said information received.
 19. The method according to claim18, further comprising tracking over time a position of each of said atleast one of localized image regions or spots from said informationreceived.
 20. The method according to claim 19, further comprisingrecovering spectral information registered with each of said at leastone of localized image regions or spots from said information received.